# LINR 1 | Lesson 1 | Making Connections (Tables)

## Tables

How can you use the pattern’s table to find the slope?

• When a table represents a linear pattern, the slope can be found by computing the ratio of the change in $$y$$ and the change in $$x$$.
• One way to compute the slope in linear tables is to order the $$x$$-values so that they increase by equal increments.  When arranged in this manner, the change in the $$x$$-values and the $$y$$-values can be computed and used in the ratio to determine slope.

The computation for the slope for Pattern 1 is shown in the table below where x represents the step and y represents the number of squares in that step. Tables are created using Desmos.com. $slope=\frac{\Delta y}{\Delta x} =\frac {rise}{run}=\frac {+2}{+1}=2$

• Another way to compute the slope from a table is to choose any two points and compute the ratio of the change in $$y$$ and the change in $$x$$ between these two points.
• For example, choosing the points $$(1,6)$$ and $$(4,12)$$ from the table above, we can find the change in $$y$$ and the change in $$x$$:

$slope=\frac{\Delta y}{\Delta x}=\frac{(12-6)}{(4-1)}=\frac {6}{3}=2$

• This method defines the formula for finding slope between any two points on a line where the first point is defined as $$(x_1,y_1)$$ and the second point is defined as $$(x_2,y_2)$$:  $slope=\frac{(y_2-y_1)}{(x_2-x_1)}$

1. Compute the slope for the remaining patterns by ordering the $$x$$-values in each table or by choosing two points and using the slope formula.

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